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MINISTRY OF EDUCATION AND TRAINING MINISTRY OF AGRICULTURE AND RURAL DEVELOPMENT VIETNAM NATIONAL UNIVERSITY OF FORESTRY LUONG ANH TUAN STUDY ON THE DYNAMICS OF FIRE FIGHTING MOTORCYCLES FOR THE OLD QUARTERS IN HANOI CITY MAJORITY: MECHANICAL ENGINEERING CODE NO: 9520103 SUMMARY OF ENGINEERING DOCTORAL THESIS Ha Noi, 2022 Research work is completed at: Vietnam National University of Forestry Scientific instructors: Assoc Prof Dr TAI VAN DUONG Dr SON HOANG Reviewer 1: Reviewer 2: Reviewer 3: The defense will be taken in front of the Institutional Board of Thesis Evaluation at: Vietnam National University of Forestry At: … time, Date ….Month… year 2022 The thesis can be found in the libraries: National Library; Library - Vietnam National University of Forestry; Library - Vinh Long University Of Technology Education INTRODUCTION The urgency of the thesis To meet the requirements of fire fighting equipment for the old town area, where there are narrow roads and small alleys in crowded residential areas, the University of Fire Prevention has researched, designed and manufactured successfully Fire fighting motorcycles are used in the old town areas, in narrow alleys, after researching and manufacturing, they have been used in some localities such as Hanoi and Ho Chi Minh City for good fire fighting effect In the process of using a fire fighting motorbike, there are many problems such as the front wheel of the vehicle being split when starting or when crossing a bump on the road, the vehicle may overturn when turning around in narrow alleys, vibrating shaking the steering wheel when the vehicle is in motion makes it difficult for the driver From the existence of the above-mentioned fire fighting motorcycles, it is necessary to study the dynamics of fire fighting motorcycles for the old quarters to serve as a scientific basis for the design and manufacture of fire engines for the old town areas, narrow alleys Stemming from the above reasons, the thesis conducted a study with the title: "Study on the dynamics of fire fighting motorcycles for the old quarters in Hanoi city" Research objective of the thesis Building a scientific basis to serve the calculation, design and manufacture of fire fighting motorcycles for the old quarters to meet the requirements of balance and stability of the vehicle when moving in narrow alleys, to improve the mobility of fire engines Research subject The research object selected by the thesis is the fire-fighting motorcycle for the old quarters, designed and manufactured by the Ministry of Public Security and used in some localities Research scope - Building models, doing theoretical and experimental research to find out some parameters for mounting specialized equipment for rescue and fire fighting in vehicles Ensure the vehicle's movement is stable, gripping, not shaking and easy to drive - Build a kinematic model to calculate the vehicle's ability to move through narrow corners and corners, as a basis for planning rescue and fire fighting movements in the area New contributions of the thesis The thesis has built a model and established a system of equations for the linear motion of the fire engine when starting and moving through the road surface, the results of the survey of the dynamic equation of the fire engine The fire engine has determined a number of reasonable parameters: the height coordinates of the center of gravity of the equipment cluster according to the height Zm= 75cm, the coordinates of the center of gravity of the equipment cluster along the X axis is X m= 15cm, then the wheel In front of the vehicle, the vehicle always clings to the road at all speeds ≤ 70km/h and the load of the fire fighting equipment assembly on the vehicle can be up to 130kg Having built a kinematic calculation model of a fire engine when turning around, when moving through a narrow alley, a formula for calculating the kinematic parameters of the vehicle has been established: speed , angle of inclination , investigated the kinematic equation of the vehicle moving through narrow bends, from the survey results, a table of safe speeds corresponding to the coefficient of sliding friction and turning radius was obtained from the survey results (Table 3.2) and the size table of vehicle length corresponding to the vehicle width of 1m (table 3.3) The thesis has developed an experimental research method and determined a number of dynamic parameters of the fire engine, including: coordinates of the vehicle's center of gravity, the stiffness of the shock absorber, the moment of inertia , deformation of the front tire, displacement of the driver's body, experimental results to verify the theoretical model and complete calculation of the fire engine Scientific and practical significance of the thesis 6.1 Scientific significance of the thesis The research results of the thesis have built a scientific basis to calculate the design and manufacture of fire fighting motorcycles in the old town, and at the same time, the thesis has built an empirical research methodology to determine a number of parameters dynamics of fire engines From the results of theoretical and experimental research, it is possible to make scientific documents for calculating and determining the reasonable values of some parameters of fire engines 6.2 The practical significance of the thesis The research results of the thesis are used for the design, manufacture and completion of fire fighting motorcycles for the old quarters and narrow alleys, in addition, they are also used as a reference for the design research Design and manufacture other specialized motorcycles Chapter OVERVIEW OF RESEARCH ISSUES 1.1 Overview of research works on the dynamics of motorcycles 1.1.1 Research works on the dynamics of motorcycles in the world The author Sharp, R.S published the article "Stability, control response and steering of a motorcycle" [31], the author established the equation of stability of the vehicle when the motorcycle was moving in a straight line with the response of motorcyclists, this study applies to motorcycles without cargo Author Koenen, C published the doctoral thesis, Delft University: "Motorcycle dynamics when running straight ahead and when cornering" [32], the author built a model and established equations for motorcycles when the vehicle is moving in a straight line and when the vehicle enters a roundabout with a change in vehicle speed, the study is for the vehicle without cargo Breuer, T and Pruckner, A., published work [34], which performed advanced dynamics analysis and motor simulation, which investigated the factors affecting the dynamics of motorcycles motorcycles and simulated motorcyclists on Matlab-Simulink software, the work has not analyzed the dynamics of fire engines Sharp, R.S, Limebeer, D.J.N., published the work [35], the work introduced a motorcycle model to analyze the stability and control control parameters for the case of the car moving on a straight road at a constant speed In summary: In the world, there have been a number of published studies on motorcycle dynamics, after which the above-mentioned studies mainly focus on the study of motorcycles without cargo, there is no research work on fire fighting motorcycles, special-use motorcycles 1.2 Research projects on fire fighting motorcycles in Vietnam Dr Le Quang Bon University of Fire Prevention has successfully carried out a project at the Ministry of Public Security: "Research, design, and manufacture multi-function fire fighting and rescue motorcycles" [3], the results of The project has successfully designed and manufactured a multifunction fire fighting and rescue motorcycle, this fire engine has been put into use in the old quarters of Hanoi, Hoi An and Ho Chi Minh City The research results of the topic only focus on the design and manufacture, there is no study on the dynamics of fire fighting motorcycles Assoc Prof Dr Duong Van Tai has successfully researched forest fire fighting motorbikes, the research results have designed, manufactured and commercialized fire fighting motorbikes for a number of localities such as Forest Rangers of Binh Phuoc Province, Forest Rangers of Thua Thien Hue Province Thien Hue, Management Board of Protection Forests and Special-Use Forests in Hanoi [24] In summary: In Vietnam, there have been a number of research works on fire fighting motorcycles, however, the works only focus on design and manufacture without any research on the dynamics of fire engines 1.3 Research objectives of the thesis From the research results obtained in the overview, the thesis sets out the following research objectives: Building a model, setting up a system of differential equations for the motion of a fire engine when moving on a straight line and in a corner, surveying a system of dynamic differential equations, to serve as a scientific basis for the process of calculating and designing the old town fire fighting motorbike in order to improve the vehicle's maneuverability Chapter DYNAMIC FACILITIES OF FIRE MOTORCYCLE 2.1.2 General arrangement of fire engines The general design model for a multi-purpose fire, rescue and rescue vehicle is shown in Figure 2.1 Figure 2.1: General layout of a multi-purpose fire, rescue and rescue motorcycle 1- Priority whistle; 2- Priority flash; 3- Base vehicle (Kawasaki W175); 4Container for fire fighting tools; 5- Electric kickstands keep the vehicle balanced during fire fighting activities; 6- Generator; 7- Containers containing fire-fighting hoses; 8- Honda GX160 T2 engine fire pump; 9Priority mast lights; 10– Powder fire extinguisher; 11- Portable intermediate water tank; 12- Roll of water suction hose; 13- Support frame; 14- Box containing multi-purpose demolition tools, drills, lights, gas masks From the general structure model of the fire fighting motorcycle shown in Figure 2.1, the thesis proceeds to build a dynamic model of the motorcycle when it is moving on a straight road and in a narrow alley 2.2 Building a model, setting up the dynamic equation of the motorcycle when moving on a straight road 2.2.1 Flat motion model of fire fighting motorcycle The flat motion model of the motorcycle is simulated by pieces of hardware: Suspension block (including chassis, engine, driver, fire and rescue vehicle assembly, slider of the front fork), lower fork of the front fork , rear fork, front wheel, rear wheel These parts are linked together through rotary joints, translational joints Elastic coefficient and damping coefficient: Cbr , kbr for the rear wheel and Cbf , kbf for the front wheel The rear and front shock absorbers have elastic coefficients and damping coefficients respectively : Cr , kr and C f , k (Figure 2.2) f Choose the overall coordinate system O 1xyz, whose origin O1 is located at the contact position between the rear tire and the road surface, the x-axis is in the direction of the vehicle's forward direction, and the z-axis is up With the coordinate system selected as above, we have table - the symbols of the centroids of the clusters and their coordinates at the initial time (t=0) and at the time of consideration t Figure 2.2: Plane motion model of fire truck Table 2.1 Symbols for centroids, masses, initial coordinates and coordinates at time t of the blocks Moment of inertia about an axis parallel to and through the center of gravity of the rotating blocks:Suspension IG ,later IGr , cluster under front fork IGf Let the outer radius of the rear and front wheels be Rr and Rf If in the coordinate plane O1xz, the road surface has the equation z = f(x) and rear wheel axle R, front wheel axle F have coordinates of ( xR ,zR )and ( xF ,zF ) then the symbol dr =zR – f(xR) - Rr and df =zF – f(xF) – Rf (Figure 2.2) The pavement equation Z = f(x) is used in the calculation, in case the pavement has a slope of α, the pavement equation will be:Z=X.tanα The physical meaning of the quantities dr , df: + Is the deformation of the rear and front tires (in the direction of the wheel radius) if they are negative; + Is the distance from the road surface to the outside of the rear and front tires if they have a non-negative value Thus, the front wheel is in contact with the road surface when the quantity df is negative 2.2.4 Equation of motion of a fire engine on a straight line Lagrange function: L = T - П , and q     z z G T is the general lagrang F coordinates, resulting in a system of equations of motion: d  T  T  Wd i dt q  Q  q  q q  i i i i (2.37) Substituting the expressions (2.18)-(2.36) into (2.37) leads to a system of equations of motion of the form: M q, q.q  P q, (2.38) q By notation as above, the matrix M and P have the form:  A11  A1 A1 A14    T  Wd    QV      ;        x  L , L  L  x 0 Here, H=0,3 (m) is the height of the bumper, L =0,5 (m), L0 = 20 (m), (Figure 3.2) Evaluate the phenomenon of vehicle loading (the front wheel is not in contact with the road surface) through the quantity d f = zF – f(xF) - RF, where (xF,zF) is the coordinate of the front wheel axis and R F is the outer radius of the front tire The front tire grips the road when d f < and does not contact the road when df ≥ Note that, there is always df ≥ -hb where hb is the maximum deformation of the front tire, in the calculation here take h b = 0.02 (m) Figure 3.1: Description of road surface bump in length The survey problem with two ways to change the speed of the rear wheel of the vehicle is described in Figure 3.2 as: The law of linear speed change of the wheel is: vR  25 18 t , ( m / s ) (3.8) The law of nonlinear velocity change (i.e acceleration varies with time), 505  expressing velocity has the form:   t 1 15 1 ,( m / (3.9) v s) R 18   Figure 3.2: Describe two ways of changing vehicle speed over time Line 1: Law of linear velocity change equation (3.8) Line 2: Nonlinear velocity change law equation (3.9) a) Survey with the law of speed change and the vehicle through the bumpy road surface Survey with the mass of equipment cluster mM = 90kg on two types of flat roads without obstacles and with burrs with two ways of changing the speed (1), (2) in Figure 3.3, when the xM value changes gave the following df value: Figure 3.3: Graph df corresponding to speed according to the rule (3.8) without obstacles: f(x) = Figure 3.4: Graph df corresponding to the speed according to the rule (3.9) without obstacles: f(x) = Figure 3.5: The graph of df corresponding to the speed according to the rule (3.8) has a barrier : f(x) > Figure 3.6: The graph of df corresponding to the speed according to the rule (3.9) has a barrier : f(x) > From the survey results obtained in Figures 3.3 to Figure 3.6, the following observations are made: There are no barriers on the road surface in the graphs of Figure 3.3 and Figure 3.4 + The vehicle's ability to grip the road is reduced when the xM value is smaller (ie, the closer the vehicle cluster is installed to the rear) + With the way to change the speed according to the rule (3.8) (road (1) figure 3.2 gives better ability to grip the road than the way to change the speed according to the rule (3.9) (road (2) figure 3.2 the law of speed change (3.8), the car clings to the road surface at all speeds when xM ≥ (figure 3.3), but with the law of speed change (3.9) with xM = 0, the front wheel does not stick to the road when vehicle at speed v > 50km/h (Figure 3.4) On a bumpy road with a height of 30cm and a width of 0.5m (Figure 3.1), all vehicles pass at a speed greater than 25km/h (Figure 3.5 - Figure 3.6) b) Survey with the change in mass of the fire fighting equipment assembly on the vehicle Investigate the model with different mass of equipment: Change the speed according to the road rule (1) in Figure 3.2, the car runs on a flat road without obstacles, the mass of the instrument cluster mM= 90, 110, 130(kg); xM = 0(m) and xM = 0,15(m) Figure 3.7: df graph corresponding to different mass mM, with velocity according to the rule (3.8), xM = 0(m) and no barrier : f(x) =0 Figure 3.8: df graph corresponding to different mass mM, with speed according to the rule (3.8), xM = 0,15(m) and no barrier: f(x) =0 Comment: When xM = 0,15(m), the front wheel of the car still grips the road at all speeds of 70km/h and the mass of the instrument cluster can carry up to 130kG, while xM = 0(m) the wheel can carry up to 130kG The front of the car only grips the road with a mass of 90kg 3.2 Calculation of the speed of the fire engine when turning around Assuming the coefficient of sliding friction between the tire and the road surface is µ, then according to (2.48), if the vehicle moves around a curve of radius Rc, the vehicle speed must satisfy: here g = 9,81 (m/s2) v  gRc , (3.10) If the curve on the road has a width of a, then the radius of the turn Rc < a Table 3.2 gives some maximum vehicle speeds when turning around bends with radius Rc corresponding to values of coefficient of sliding friction µ Table 3.2 Maximum vehicle speed vmax (km/h) when passing a bend with radius Rc (m) corresponding to coefficients of sliding friction µ Chapter EXPERIENCE TO DETERMINATE THE PARAMETER OF FIRE MOTORCYCLES, VERIFY THE THEORY CALCULATION MODEL 4.1 Objectives of experimental research - Determination of numerical values of some quantities, some coefficients in the systems of dynamic equations for linear motion and diversion of fire engines, to serve the investigation of the established theoretical model set up in chapter - Test a number of theoretical results from which to evaluate the reliability of the established dynamics model 4.2 Experimental research tasks To achieve the above goal, experimental research must perform the following tasks: - Determine the coordinates of the center of gravity of the fire engine; - Determine vehicle length, vehicle weight base; - Determine the stiffness coefficient and damping coefficient of the front and rear shock absorbers; - Determine the stiffness and damping coefficients of the front and rear tires; - Determine the center of gravity of the vehicle: - Determine the moment of inertia about the horizontal axis passing through the center of mass of the blocks: - Actual testing of the front tire deformation calculation model df at different speeds 4.3 Experimental results to verify the theoretical computational model 4.3.1 Organize and conduct experiments * Measure tire deformation in straight movement - The experimental site at Vietnam Specialized Equipment Joint Stock Company is located at Xuan Mai - Chuong My - Hanoi - Test site: The test is carried out on a straight line, without slope, the parameters of the vehicle are similar in Table 3.1 and Table 3.2 * Experimental layout Devices for measuring front tire settlement include: (a) Encoder E6B2-CWZ6C with output 2000 square pulses/revolution (b) Central processor using STM32 microcontroller with kid's board programming in C language The measuring device includes 02 wireless transceivers and signal amplifiers, 01 set of Encoder E6B2-CWZ6C, 01 set of Spider8 (with signal receiving channels), 01 computer installed with specialized software for Spider Location of experimental equipment is shown in Figure 4.23 1)- The first wireless transmitter (with an input connected to the pressure gauge tenzo glued to the outside of the front tire) attached to the spokes, rotating with the wheel; (2)- The coupled pressure tenzo connected to a wire that is glued to the outside of the tire; (3)- The antenna receives the signal from the transmitter; (4)- Amplifier of received signal; (5)- The signal port from the amplifier to the Spider8 according to the principle of parallel signal transmission; (6)-The signal port from Spider8 to PC according to the principle of serial signal transmission (RS-485); (7) Spider8; (8) – Computer * Experimental organization Place the Encoder fixed on the vehicle and coaxial with the front wheel (via the speedometer wire) The output signal of the encorder is connected to the second wireless transmitter located on the vehicle Signal receiving and processing side: Signals transmitted from two wireless transmitters (with two different frequencies) are received through two antennas to two signal amplifiers (which are part of the Spider 8)'s peripherals The signal from the amplifier is fed to the Spider through the parallel communication port (8 bits) Next Spider is communicated with the PC through the parallel communication port (RS-485) as shown in Figure 4.23(b) Catman specialized software for Spider is designed to be able to store data, export data to excel or matlab files for calculation and graphing From Spider 8's dedicated Catman software set the time to count pulses t =1(s) The formula for velocity is calculated as follows: v n t.2000 (rpm) , n is the total number of pulses counted Figure 4.24: Experimental measuring the deformation of the front wheel tire Testing data is recorded in Appendix 04, in which the quantities: t, VR-TN, dfTN are time, speed and df are calculated through testing The discrete data of the VR-TN velocity measured through the experiment (described by the "+" signs in Figure 4.24) to be used to test the theoretical computational model, they need to be described below form of a dependent function t (described by a continuous curve in Figure 4.24) Using the least squares method, the vehicle speed is expressed as a quadratic function VR_QH dependent on t Applying the law of acceleration VR_ QH to the theoretical model, after the calculation, the corresponding df_LT value is obtained The graph of df _TN and df_LT values depending on the velocity is shown in Figure 4.25 Compare the correlation coefficient between two ranges of values df _TN and df_LT to draw conclusions about whether the theoretical model is consistent with reality or not The experimental process is shown in Figure 4.24 4.3.2 Method of determining the deformation of the tire df The deformation of the front tire (the settlement df) is determined by the following formula: d  f Nf Cbf (4.17) Where: Nf - Pressure of the road surface on the tire (measured through tenzo) Cbf - Coefficient of stiffness of the front tire 4.3.3 Verifying the theoretical computational model Experimental results are performed with a device cluster with a mass of 90 kg, the VR -TN velocity changes according to the rules of Figure 4.25a with xM=0.15m, Figure 4.25b with xM=0 Corresponding to the measured VR-TN values during the experiment, by the least squares method, there is a VR-QH formula that describes the rule of VRTN over time: With figure 4.25a :VR-QH = 0,010273.t2 + 4,91019.t + 0,102312 (4.18) With figure 4.25b : VR-QH = -0,20847.t2 + 7,579875.t + 7,576897 (4.19) Figure 4.26: The df-TN value measured from the assay and the df-LT value calculated by the model Note that, when testing, only df < values were recorded, so in Figure 4.25b, the graph of df -TN only reached VR = 50 km/h because then the front wheel did not stick to the road surface anymore From the obtained data, it is found that the series of values of df -TN and df LT (recorded in part I of the appendix) have a correlation coefficient of 0.99 for both cases xM =0,15m and xM=0 This proves that the model of flat motion of the motorcycle is consistent with reality Through model survey and actual test with the base bike, Kawasaki W175 SE, it was found that: let the front wheel always stick to the road surface when the vehicle is running and overcome the ledge with a height of H = 0,3m with the speed v ≤ 70 km/h and the mass of the device cluster carrying mM ≤130kG, it is necessary to satisfy the condition xM ≥ 0,15m Due to the design of the fixed base vehicle, the value cannot be changed z and greater than 0,15m Therefore, the best location for mounting the M xM instrument cluster is xM = 0,15m and zM = z M CONCLUSIONS AND RECOMMENDATIONS Conclusion After obtaining the research results, the thesis draws the following conclusions: From the structure and operation of the fire engine, the thesis has built a plane dynamics model, established a system of equations for the linear motion of the fire engine, the results This is the basis for calculating reasonable parameters when mounting the fire fighting equipment assembly on the vehicle, ensuring stability when driving on a straight road at a speed of ≤70km/h and when going through bumpy roads The thesis has built a kinematic calculation model of the fire fighting motorcycle when turning around, established the formula for calculating the kinematic parameters of the vehicle: speed, angle of inclination , as a basis calculate the safe speed when the car goes through the corners From the kinematic equation when the vehicle turns around, the table of safe speeds corresponding to the coefficient of sliding friction and the turning radius is given (table 3.2) The kinematic model of the fire-fighting motorcycle has been built up when going through narrow bends, investigated the kinematic equation of the vehicle moving through the narrow bends, given the vehicle length dimension table corresponds to a width of 1(m) Through this result, it shows that: With a vehicle width of 1m, vehicle length L ≤ 2,2m can pass through the square corners of alleys with a width of 1,5(m) Calculation table 3.3 will serve as the basis for making rescue and fire fighting plans in the old quarter, narrow alley areas Building a model to calculate the maximum horizontal deviation of the center of gravity of the device cluster; determine the parameters to be tested to know the range of their values With these values, the maximum horizontal deviation of the center of gravity of the instrument cluster will be calculated in accordance with the driver's comfort when operating The dynamic equation of linear motion of the fire engine has been investigated, the survey results are the scientific basis for calculating and determining the reasonable values of the geometrical and structural parameters of the installation work system on a fire engine The results of the vehicle's linear motion dynamics survey show that when using the base vehicle, a Kawasaki W175 SE motorcycle, and setting the coordinate height of the center of gravity of the instrument cluster Zm=75cm (equal to the center of gravity of the suspension block with driver) then the center of gravity coordinates of the instrument cluster on the X axis of Xm=15cm will be most reasonable, then the front wheel of the vehicle always grips the road at all speeds ≤70km/h and the instrument cluster load can reach 130kg By experimental research, the thesis has determined some dynamic parameters of fire fighting motorcycles to serve the problem of surveying the system of dynamic equations of fire engines Conducted experiments to determine the deformation of the front wheel tires when starting and when moving through the pavement, the experimental results have verified the theoretical model to calculate the dynamics of the vehicle's linear motion, The results of comparing the error between the theory and the experiment are within the allowable limit, from the experimental results, it shows that the theoretical calculation model is reliable The research results of the thesis have been applied in practice to design and manufacture a new model of fire fighting motorcycle After being built according to the optimal calculation parameters, the fire-fighting motorcycle has overcome some limitations that are: the vehicle is stable when turning, turning left, turning right, the vehicle does not separate the front wheel before turning departure, when passing bumpy road surface Recommendations Due to the limited time of the study, in order to make the thesis more complete, it is necessary to continue to study some of the following issues: In the process of the vehicle moving on a bad, bumpy road surface, the steering system is shaken, so it is necessary to continue to study the vibration of the vehicle when the vehicle is operating on some types of roads The characteristic parameters of the tire and the driver's behavior also affect the stability of the fire fighting motorcycle, so it is necessary to continue studying the influence of the tire characteristics and the influence of human behavior Drive to the vehicle's stability LIST OF PUBLICIZED ARTICLES, SCIENTIFIC WORKS RELATED TO THE THESIS [1] Luong Anh Tuan (2020), Fire fighting motorbikes for the old quarters in Hanoi city.Vietnam Journal of Mechanics ISSN 2615-9910, No 12, 2020, pp 108-112 [2] Luong Anh Tuan (2021), Study on the dynamics of two-wheeled motorbikes dedicated to fire fighting and rescue in the old quarters of Hanoi city Vietnam Mechanical Magazine ISSN 2615-9910, No 11, 2021, pp 7885 [3] Luong Anh Tuan (2021), Studying the dynamics of the use of twowheeled motorcycles in firefighting and rescue, Proceedings of Thirtieth International Scientific – Technical Conference “SAFETY SYSTEMS 2021” November 25, 2021 Moscow, Paper 224 – 231 [4] Luong Anh Tuan (2022), Research of road grip of two-wheeled motorcycles designed for firefighting and rescue in a straight line, Опубликовано на конференции Сборник трудов секции № 8, ХХXII Международной научно-практической конференции, «ПРЕДОТВРАЩЕНИЕ СПАСЕНИЕ ПОМОЩЬ», марта 2022 года, Бумага – 16 [5] Luong Anh Tuan (2022), Multipurpose motorcycles in densely populated areas, Опубликовано ПОЖАРОТУШЕНИЕ проблемы, технологии, инновации Материалы VIII Международной научнопрактической конференции, 17-18 марта 2022 года, Бумага 19-25 [6] Vu Khac Bay, Duong Van Tai, Hoang Son, Luong Anh Tuan, Hoang Nhan (2022), Studying the road grip of firefighting and rescue motorcycles when moving straight, Published in Growing Science (Engineering Solid Mechanics), Volume 10, Paper 227 - 240 ... elastic coefficients and damping coefficients respectively : Cr , kr and C f , k (Figure 2.2) f Choose the overall coordinate system O 1xyz, whose origin O1 is located at the contact position... motorcycle: weight mg and air resistance F D acting at the vehicle's center of gravity G; thrust FR exerted by the road surface on the motorcycle at the point of contact with the rear wheel; vertical... < b (Figure 2.9) The line segment AB is the tangent to this arc intercepted by the coordinate axes Ox and Oy Find the minimum value of AB when the point of contact M moves on this arc Figure